It is with huge pleasure that I introduce today’s puzzle, which is already a big deal in Japan. It’s called Menseki Meiro, or Area Maze, and I hope you find it as brilliant as I do.

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Area Maze is the creation of Naoki Inaba, one of the world’s most prolific inventors of logic puzzles. He came up with Area Maze after being asked to come up with a puzzle by the head of a crammer school in Japan.

The puzzle is utterly simple to explain: find the missing value, which is denoted by a question mark highlighted in grey. The only mathematics you need to know is that the area of a rectangle is the length multiplied by the width.

Here’s what makes the puzzle genius: You are NOT allowed to use fractions in the solutions. If you were, you could write out lots of equations and solve them. Yuck, yuck, yuck. All Area Mazes can be solved using only whole numbers. Here’s a very simple one to get you going. If you need help with it scroll down.

Naoki Inaba has been devising puzzles since he was a teenager. He earns his living providing the Japanese media with well-known puzzles, like Sudoku, and also creating hundreds of new ones of his own. His website (in Japanese) has more than 400 original puzzles.

I asked him about Area Maze. “Calculating the areas of rectangles is not a new theme,” he said. “So I myself didn’t think I could make very interesting puzzles with it at first. Once I started making some Area Maze problems I hit upon some ideas about it one after another, and was able to make various problems – from easier ones to harder ones, and problems which need kind of inspiration to solve. Consequently, not only the children of the cram school but also many puzzle fans like it.”

Naoki Inaba infront of a shelf of his Area Maze books. Photograph: Naoki Inaba

Ill be back later today to show you how to solve the more difficult puzzles.

Meanwhile, here’s how to solve the very first one.

The trick is to complete the large rectangle, as below. We know that the area A must be 20cm, since it is 4 x 5. Which means that A + the rectangle below it has area 20 + 16 = 36cm. This area is the same as the large rectangle on the left side. Since they share the same height, they must share the same width - so the missing value is 5cm.